You can wash rubber Mats the same way you wash your car, just don’t use the same mitt / sponge on the paint work afterwards.
There is many products out there to maintain plastic / rubber but I would not recommend using any of these products on your mats as most are designed for external use, also the last thing you want is silicone on your shoes \ pedal that is a recipe for disaster.
Your best bet is to buy some carpeted mats and keep your rubber ones for when you require more internal protection?